K. Koepernik

The Kohn-Sham equation of state for elemental solids: a solved problem

K. Lejaeghere, G. Bihlmayer, T. Björkman, P. Blaha, S. Blügel, V. Blum, D. Caliste, I.E. Castelli, S.J. Clark, A. Dal Corso, S. de Gironcoli, T. Deutsch, J.K. Dewhurst, I. Di Marco, C. Draxl, M. Dułak, O. Eriksson, J.A. Flores-Livas, K.F. Garrity, L. Genovese, P. Giannozzi, M. Giantomassi, S. Goedecker, X. Gonze, O. Grånäs, E.K.U. Gross, A. Gulans, F. Gygi, D.R. Hamann, P.J. Hasnip, N.A.W. Holzwarth, D. Iușan, D.B. Jochym, F. Jollet, D. Jones, G. Kresse, K. Koepernik, E. Küçükbenli, Y.O. Kvashnin, I.L.M. Locht, S. Lubeck, M. Marsman, N. Marzari, U. Nitzsche, L. Nordström, T. Ozaki, L. Paulatto, C.J. Pickard, W. Poelmans, M.I.J. Probert, K. Refson, M. Richter, G.-M. Rignanese, S. Saha, M. Scheffler, M. Schlipf, K. Schwarz, S. Sharma, F. Tavazza, P. Thunström, A. Tkatchenko, M. Torrent, D. Vanderbilt, M.J. van Setten, V. Van Speybroeck, J.M. Wills, J.R. Yates, G.-X. Zhang, S. Cottenier


The success of modern density-functional approximations to electronic-structure theory has led to a wealth of
general-purpose codes, allowing researchers to tackle a wide range of applications. Given this extensive usage
by the scientific community, it is striking that it has never been thoroughly investigated to what extent results
vary over different implementations: do different approaches to density-functional theory really yield identical
predictions for a given exchange-correlation functional? We report the results of a community-wide effort that
compares 15 different codes using 40 different potentials or basis set types to assess the quality of the Perdew-
Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that codes and pseudopotential
datasets have only recently achieved error bars of 1-2 meV/atom for solids. Hence, we have only now come to
a level where the differences between most implementations of the Kohn-Sham equations for a given functional
are comparable to the uncertainty in a high-precision experimental determination of the equation of state.

Electron penetration into the nucleus and its effect on the quadrupole interaction

K. Koch, K. Koepernik, D. Van Neck, H. Rosner, S. Cottenier
Physical Review A
81, 032507


series expansion of the interaction between a nucleus and its surrounding electron distribution provides terms that are well-known in the study of hyperfine interactions: the familiar quadrupole interaction and the less familiar hexadecapole interaction. If the penetration of electrons into the nucleus is taken into account, various corrections to these multipole interactions appear. The best known correction is a scalar term related to the isotope shift and the isomer shift. This paper discusses a related tensor correction, which modifies the quadrupole interaction if electrons penetrate the nucleus: the quadrupole shift. We describe the mathematical formalism and provide first-principles calculations of the quadrupole shift for a large set of solids. Fully relativistic calculations that explicitly take a finite nucleus into account turn out to be mandatory. Our analysis shows that the quadrupole shift becomes appreciably large for heavy elements. Implications for experimental high-precision studies of quadrupole interactions and quadrupole moment ratios are discussed. A literature review of other small quadrupole-like effects is presented as well (pseudoquadrupole effect, isotopologue anomaly, etc.).

Open Access version available at UGent repository
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